common law Spouse i
No, it's not the same thing, not as you described it anyway. You said:
a spouse who cohabits with another on the bonafide belief that he or she is lawfully married to the other person
That sounds like somebody delusional, 'believes' they're married. You're either married or you're not. As for common law spouse, that status can only exist in a country that has common law as part of its legal system. Poland doesn't. Also, a common law spouse in the handful of countries where that status is acknowledged has certain legal rights and entitlements if they're a citizen of that country but those rights are limited and they are not treated as a full, legal marriage partner. Anyway, as far as immigration in Poland is concerned, no you can't bring your girlfriend to Poland if she's not an EU or EEA citizen, as a family member or dependent.